Is there a shortcut to repeat the last operation in Blender
Yes.

F3 will give you a list of recent actions. After selecting one action from the list, the next time you press F3 the list will be positioned with the same action under the cursor. This makes it very easy to call the same action over and over quickly by pressing F3 LMB (without having to move the mouse), or F3&#9166; Enter.

In the 3D view you can call the previous action with &#8679; ShiftR, however this doesn't seem to work in the UV editor.



Another option is to add a custom shortcut for the align operators.

To do this add a new shortcut in &#9096; Ctrl&#9095; AltU> User preferences > Input. You probably want to define it in some reasonable context like Image > UV editor, so expand the corresponding sections and click New shortcut at the bottom of the UV editor section. 

Then put uv.align as the operator and assign a key combination:



Note that you also have the option to change the various parameter the operator is called with when the shortcut is pressed (though in this case there is only one parameter):



Even if the drop down appears grayed out, you can probably still change it. It will appeared grayed out if no parameter is specified, in which case the default it used.

Also see: How to add shortcut for &#39;Only Render&#39;?